R上自相似集的自相似测度的局部维数探讨  

Research of the Local Dimension of Self-similar Measure on the Self-similar Set in R

作　　者：熊波[1] 邓薇[1] 孙丽[1] 

机构地区：[1]中南财经政法大学信息学院,湖北武汉430074

出　　处：《长江大学学报（自科版）（上旬）》2010年第1期17-20,共4页JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG

基　　金：上海市科委启明星计划(03QA14036)

摘　　要：研究了R上满足开集条件的一族压缩映射所生成的自相似集,讨论了其上给定的自相似测度μ的局部维数,在R中解决了Cawley和Mouldin问题。证明了在R中若{Ti(x)}in=1满足开集条件,x∈G∩K,Cawley和Mouldin猜想成立,并且举出反例子验证当存在x∈G/K时,Cawley和Mouldin猜想不成立。The self-similar set generated by a family of contracting maps satisfying the open set conditions was studied,on this self-similar set,the local dimension of the self-similarity measure μ was discussed for solving the problem of Cawley and Mouldin in R.It proves that if {Ti(x)}ni=1 satisfy the open set conditions in R,x∈G∩K,the guess of Cawley and Mouldin is right,it gives an example to show existing x∈G∩K such that the guess is not right.

关 键 词：自相似集 自相似测度 局部维数 开集 压缩映射 Cawley和Mouldin猜想 

分 类 号：O174.1[理学—数学]